Networks with Periodic Interactions

We consider a mathematical model of genetic regulatory networks (GRN). This model consists of a nonlinear system of ordinary differential equations. The vector of solutions X(t) is interpreted as the current state of a network for a given value of time t. The evolution of a network and future states depend heavily on the attractors of a system of ODE. We discuss this issue for low-dimensional networks and show how the results can be applied to the study of large-size networks. Examples and visualizations are provided. The remarkable feature of our research is that the interactions in a network are supposed to be variable. We focus on the interaction of variable activation-inhibition cycles.